Block #2,816,331

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/30/2018, 4:56:58 AM · Difficulty 11.6866 · 4,010,751 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

163754efc3b5b7e8d553d2d36a566eb05b480a8df0a5d5c59ff00daf9c2473e3

View on Chainz ↗

Height

#2,816,331

Difficulty

11.686610

Transactions

Size

428 B

Version

Bits

0bafc5ad

Nonce

212,406,293

Timestamp

8/30/2018, 4:56:58 AM

Confirmations

4,010,751

Mined by

⛏️ P2SHAeVxGWu725W85TjphPWtRBUjm2ZxAgaD5h

Merkle Root

ed59098d4a84a214c9569728edb88cb8fa7f4a111467d3713ea1147aee848ed5

Transactions (2)

Coinbasebf36bac2a42344…b0485cfcff1b41

1 in → 1 out7.3200 XPM110 B

AeVxGWu7…ZxAgaD5h

d1885194515371…29f03555e2c60c

1 in → 2 out3.6428 XPM226 B

AUqXAsGB…NzuSaTot AKGxoSP8…8oH3hVLd

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.592 × 10⁹⁹(100-digit number)

15922919812036623690…36213230503705968639

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.592 × 10⁹⁹(100-digit number)

15922919812036623690…36213230503705968639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.592 × 10⁹⁹(100-digit number)

15922919812036623690…36213230503705968641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.184 × 10⁹⁹(100-digit number)

31845839624073247381…72426461007411937279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.184 × 10⁹⁹(100-digit number)

31845839624073247381…72426461007411937281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.369 × 10⁹⁹(100-digit number)

63691679248146494763…44852922014823874559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.369 × 10⁹⁹(100-digit number)

63691679248146494763…44852922014823874561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.273 × 10¹⁰⁰(101-digit number)

12738335849629298952…89705844029647749119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.273 × 10¹⁰⁰(101-digit number)

12738335849629298952…89705844029647749121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.547 × 10¹⁰⁰(101-digit number)

25476671699258597905…79411688059295498239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.547 × 10¹⁰⁰(101-digit number)

25476671699258597905…79411688059295498241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.095 × 10¹⁰⁰(101-digit number)

50953343398517195810…58823376118590996479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,816,331

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